Investigating the Metallicity-Mixing Length Relation

TL;DR

This study uses asteroseismic data to empirically determine how the mixing length parameter varies with stellar properties, improving stellar models by providing a more accurate relation than the solar-calibrated value.

Contribution

It introduces a new empirical linear relation for the mixing length parameter based on a large stellar sample, considering different model physics and comparing with previous studies.

Findings

The mixing length parameter varies with stellar properties.

A linear model approximates the relation between $\alpha$ and stellar parameters.

Comparison with 3D simulations and previous studies validates the relation.

Abstract

Stellar models typically use the mixing length approximation as a way to implement convection in a simplified manner. While conventionally the value of the mixing length parameter, $\alpha$, used is the solar calibrated value, many studies have shown that other values of $\alpha$ are needed to properly model stars. This uncertainty in the value of the mixing length parameter is a major source of error in stellar models and isochrones. Using asteroseismic data, we determine the value of the mixing length parameter required to properly model a set of about 450 stars ranging in $\log g$, $T_{\mathrm{eff}}$, and $\mathrm{[Fe/H]}$. The relationship between the value of $\alpha$ required and the properties of the star is then investigated. For Eddington atmosphere, non-diffusion models, we find that the value of $\alpha$ can be approximated by a linear model, in the form of $\alpha/\alpha_{\odot}=5.426 -0.101 \log (g) -1.071 \log (T_{\mathrm{eff}}) + 0.437 (\mathrm{[Fe/H]})$. This process is repeated using a variety of model physics as well as compared to previous studies and results from 3D convective simulations.